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19edo Modes

Edit 0 26 …
Some scales and modes available in 19edo. Please add more, discovered or newly-composed!

Note names in 19edo

The charts below primarily use the following note names (based on standard meantone/Pythagorean notation):
0
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
C
 Ç
C# (Δb)
 ΔÇ# (Db)
 D
 Þ
D# (εb, Sb)
 ε, S
Þ# (Eb)
 E
 E# (Fb)
 F
 ϕ
F# (Γb)
 Γϕ# (Gb)
 G
 Z
G# (αb)
 αZ# (Ab)
 A
 Æ
A# (βb, Bb)
 Æ#β ,B(b)
 B, H
 B#, H# (Cb)
Note that E#=Fb and B#=Cb, but other notes are not enharmonic (for example, C# and Db are different; and E# is not the same as F). Double flats and sharps may be used as in "standard" notation; for example; Fx=F##=Gb and Bbb=A#.

Other systems of notation are of course possible, and may be preferred depending on the scales you are working with!


Meantone


meantone[5] (2L+3s / chroma-positive generator = 8\19 ~= 4/3)
UDP
 steps
 degrees
 note names
 comments
4|0
 5 3 5 3 3
 0 5 8 13 16
 C Eb F Ab Bb
3|1
 5 3 3 5 3
 0 5 8 11 16
 C Eb F G Bb
 minor pentatonic
2|2
 3 5 3 5 3
 0 3 8 11 16
 C D F G Bb
1|3
 3 5 3 3 5
 0 3 8 11 14
 C D F G A
0|4
 3 3 5 3 5
 0 3 6 11 14
 C D E G A
 major pentatonic

meantone[7] (5L+2s / CPG = 11\19 ~= 3/2)
UDP
 steps
 degrees
 note names
 mode name
6|0
 3 3 3 2 3 3 2
 0 3 6 9 11 14 17
 C D E F# G A B
 Lydian
5|1
 3 3 2 3 3 3 2
 0 3 6 8 11 14 17
 C D E F G A B
 Ionian
4|2
 3 3 2 3 3 2 3
 0 3 6 8 11 14 16
 C D E F G A Bb
 Mixolydian
3|3
 3 2 3 3 3 2 3
 0 3 5 8 11 14 16
 C D Eb F G A Bb
 Dorian
2|4
 3 2 3 3 2 3 3
 0 3 5 8 11 13 16
 C D Eb F G Ab Bb
 Aeolian
1|5
 2 3 3 3 2 3 3
 0 2 5 8 11 13 16
 C Db Eb F G Ab Bb
 Phrygian
0|6
 2 3 3 2 3 3 3
 0 2 5 8 10 13 16
 C Db Eb F Gb Ab Bb
 Locrian

meantone[12] (7L+5s / CPG = 8\19)
UDP
 steps
 degrees
 note names
 comments
11|0
 2 2 1 2 1 2 2 1 2 1 2 1
 0 2 4 5 7 8 10 12 13 15 16 18
 C Db D# Eb E# F Gb G# Ab A# Bb B#
C Δ Þ S E# F Γ Z α Æ β B#
10|1
 2 2 1 2 1 2 1 2 2 1 2 1
 0 2 4 5 7 8 10 11 13 15 16 18
 C Db D# Eb E# F Gb G Ab A# Bb B#
C Δ Þ S E# F Γ G α Æ β B#
9|2
 2 1 2 2 1 2 1 2 2 1 2 1
 0 2 3 5 7 8 10 11 13 15 16 18
 C Db D Eb E# F Gb G Ab A# Bb B#
C Δ D S E# F Γ G α Æ β B#
8|3
 2 1 2 2 1 2 1 2 1 2 2 1
 0 2 3 5 7 8 10 11 13 14 16 18
 C Db D Eb E# F Gb G Ab A Bb B#
C Δ D S E# F Γ G α A β B#
7|4
 2 1 2 1 2 2 1 2 1 2 2 1
 0 2 3 5 6 8 10 11 13 14 16 18
 C Db D Eb E F Gb G Ab A Bb B#
C Δ D S E F Γ G α A β B#
6|5
 2 1 2 1 2 2 1 2 1 2 1 2
 0 2 3 5 6 8 10 11 13 14 16 17
 C Db D Eb E F Gb G Ab A Bb B
C Δ D S E F Γ G α A β B
 Yasser's Supradiatonic
(twelfths of 12-5 chords form C Ionian mode, elevenths of 11-4 chords form C Aeolian mode)
5|6
 2 1 2 1 2 1 2 2 1 2 1 2
 0 2 3 5 6 8 9 11 13 14 16 17
 C Db D Eb E F F# G Ab A Bb B
C Δ D S E F ϕ G α A β B
 fifths of 12-5 chords form C Ionian mode
4|7
 1 2 2 1 2 1 2 2 1 2 1 2
 0 1 3 5 6 8 9 11 13 14 16 17
 C C# D Eb E F F# G Ab A Bb B
C Ç D S E F ϕ G α A β B
 octaves of 11-5 chords form C Mixolydian mod
3|8
 1 2 2 1 2 1 2 1 2 2 1 2
 0 1 3 5 6 8 9 11 12 14 16 17
 C C# D Eb E F F# G G# A Bb B
C Ç D S E F ϕ G Z A β B
2|9
 1 2 1 2 2 1 2 1 2 2 1 2
 0 1 3 4 6 8 9 11 12 14 16 17
 C C# D D# E F F# G G# A Bb B
C Ç D Þ E F ϕ G Z A β B
 octaves of 12-5 chords form C Ionian mode
1|10
 1 2 1 2 2 1 2 1 2 1 2 2
 0 1 3 4 6 8 9 11 12 14 15 17
 C C# D D# E F F# G G# A A# B
C Ç D Þ E F ϕ G Z A Æ B
 roots of 12-5 chords form C Ionian mode
0|11
 1 2 1 2 1 2 2 1 2 1 2 2
 0 1 3 4 6 7 9 11 12 14 15 17
 C C# D D# E E# F# G G# A A# B
C Ç D Þ E Fb ϕ G Z A Æ B

Miscellaneous scales


2314144 - E# F# G# Ab B Cb D - Cartunes
1163116 - E# F Gbb A# B# C Dbb E# - enharmonic approximation


MOS scales and modes of rank-2 temperaments


Negri


negri[9] (1L+8s / chroma-positive generator = 17\19)
UDP
 steps
 degrees
 note names
 comments
8|0
 3 2 2 2 2 2 2 2 2
 0 3 5 7 9 11 13 15 17
 C D Eb E# F# G Ab A# B
7|1
 2 3 2 2 2 2 2 2 2
 0 2 5 7 9 11 13 15 17
 C Db Eb E# F# G Ab A# B
6|2
 2 2 3 2 2 2 2 2 2
 0 2 4 7 9 11 13 15 17
 C Db D# E# F# G Ab A# B
5|3
 2 2 2 3 2 2 2 2 2
 0 2 4 6 9 11 13 15 17
 C Db D# E F# G Ab A# B
4|4
 2 2 2 2 3 2 2 2 2
 0 2 4 6 8 11 13 15 17
 C Db D# E F G Ab A# B
 symmetrical, has both 4/3 and 3/2
3|5
 2 2 2 2 2 3 2 2 2
 0 2 4 6 8 10 13 15 17
 C Db D# E F Gb Ab A# B
2|6
 2 2 2 2 2 2 3 2 2
 0 2 4 6 8 10 12 15 17
 C Db D# E F Gb G# A# B
1|7
 2 2 2 2 2 2 2 3 2
 0 2 4 6 8 10 12 14 17
 C Db D# E F Gb G# A B
0|8
 2 2 2 2 2 2 2 2 3
 0 2 4 6 8 10 12 14 16
 C Db D# E F Gb G# A Bb


negri[10] (9L+1s / CPG = 2\19)
UDP
 steps
 degrees
 note names
9|0
 2 2 2 2 2 2 2 2 2 1
 0 2 4 6 8 10 12 14 16 18
 C Db D# E F Gb G# A Bb B#
8|1
 2 2 2 2 2 2 2 2 1 2
 0 2 4 6 8 10 12 14 16 17
 C Db D# E F Gb G# A Bb B
7|2
 2 2 2 2 2 2 2 1 2 2
 0 2 4 6 8 10 12 14 15 17
 C Db D# E F Gb G# A A# B
6|3
 2 2 2 2 2 2 1 2 2 2
 0 2 4 6 8 10 12 13 15 17
 C Db D# E F Gb G# Ab A# B
5|4
 2 2 2 2 2 1 2 2 2 2
 0 2 4 6 8 10 11 13 15 17
 C Db D# E F Gb G Ab A# B
4|5
 2 2 2 2 1 2 2 2 2 2
 0 2 4 6 8 9 11 13 15 17
 C Db D# E F F# G Ab A# B
3|6
 2 2 2 1 2 2 2 2 2 2
 0 2 4 6 7 9 11 13 15 17
 C Db D# E E# F# G Ab A# B
2|7
 2 2 1 2 2 2 2 2 2 2
 0 2 4 5 7 9 11 13 15 17
 C Db D# Eb E# F# G Ab A# B
1|8
 2 1 2 2 2 2 2 2 2 2
 0 2 3 5 7 9 11 13 15 17
 C Db D Eb E# F# G Ab A# B
0|9
 1 2 2 2 2 2 2 2 2 2
 0 1 3 5 7 9 11 13 15 17
 C C# D Eb E# F# G Ab A# B


Deutone


deutone[6] (1L+5s / chroma-positive generator = 16\19)
UDP
 steps
 degrees
 note names
5|0
 4 3 3 3 3 3
 0 4 7 10 13 16
 C D# E# Gb Ab Bb
4|1
 3 4 3 3 3 3
 0 3 7 10 13 16
 C D E# Gb Ab Bb
3|2
 3 3 4 3 3 3
 0 3 6 10 13 16
 C D E Gb Ab Bb
2|3
 3 3 3 4 3 3
 0 3 6 9 13 16
 C D E F# Ab Bb
1|4
 3 3 3 3 4 3
 0 3 6 9 12 16
 C D E F# G# Bb
0|5
 3 3 3 3 3 4
 0 3 6 9 12 15
 C D E F# G# A#

deutone[7] (6L+1s / CPG = 3\19)
UDP
 steps
 degrees
 note names
6|0
 3 3 3 3 3 3 1
 0 3 6 9 12 15 18
 C D E F# G# A# B#
5|1
 3 3 3 3 3 1 3
 0 3 6 9 12 15 16
 C D E F# G# A# Bb
4|2
 3 3 3 3 1 3 3
 0 3 6 9 12 13 16
 C D E F# G# Ab Bb
3|3
 3 3 3 1 3 3 3
 0 3 6 9 10 13 16
 C D E F# Gb Ab Bb
2|4
 3 3 1 3 3 3 3
 0 3 6 7 10 13 16
 C D E E# Gb Ab Bb
1|5
 3 1 3 3 3 3 3
 0 3 4 7 10 13 16
 C D D# E# Gb Ab Bb
0|6
 1 3 3 3 3 3 3
 0 1 4 7 10 13 16
 C C# D# E# Gb Ab Bb

deutone[13] (6L+7s / CPG = 3\19)
UDP
 steps
 degrees
 note names
12|0
 2 1 2 1 2 1 2 1 2 1 2 1 1
 0 2 3 5 6 8 9 11 12 14 15 17 18
 C Db D Eb E F F# G G# A A# B B#
11|1
 2 1 2 1 2 1 2 1 2 1 1 2 1
 0 2 3 5 6 8 9 11 12 14 15 16 18
 C Db D Eb E F F# G G# A A# Bb B#
10|2
 2 1 2 1 2 1 2 1 1 2 1 2 1
 0 2 3 5 6 8 9 11 12 13 15 16 18
 C Db D Eb E F F# G G# Ab A# Bb B#
9|3
 2 1 2 1 2 1 1 2 1 2 1 2 1
 0 2 3 5 6 8 9 10 12 13 15 16 18
 C Db D Eb E F F# Gb G# Ab A# Bb B#
8|4
 2 1 2 1 1 2 1 2 1 2 1 2 1
 0 2 3 5 6 7 9 10 12 13 15 16 18
 C Db D Eb E E# F# Gb G# Ab A# Bb B#
7|5
 2 1 1 2 1 2 1 2 1 2 1 2 1
 0 2 3 4 6 7 9 10 12 13 15 16 18
 C Db D D# E E# F# Gb G# Ab A# Bb B#
6|6
 1 2 1 2 1 2 1 2 1 2 1 2 1
 0 1 3 4 6 7 9 10 12 13 15 16 18
 C C# D D# E E# F# Gb G# Ab A# Bb B#
5|7
 1 2 1 2 1 2 1 2 1 2 1 1 2
 0 1 3 4 6 7 9 10 12 13 15 16 17
 C C# D D# E E# F# Gb G# Ab A# Bb B
4|8
 1 2 1 2 1 2 1 2 1 1 2 1 2
 0 1 3 4 6 7 9 10 12 13 14 16 17
 C C# D D# E E# F# Gb G# Ab A Bb B
3|9
 1 2 1 2 1 2 1 1 2 1 2 1 2
 0 1 3 4 6 7 9 10 11 13 14 16 17
 C C# D D# E E# F# Gb G Ab A Bb B
2|10
 1 2 1 2 1 1 2 1 2 1 2 1 2
 0 1 3 4 6 7 8 10 11 13 14 16 17
 C C# D D# E E# F Gb G Ab A Bb B
1|11
 1 2 1 1 2 1 2 1 2 1 2 1 2
 0 1 3 4 5 7 8 10 11 13 14 16 17
 C C# D D# Eb E# F Gb G Ab A Bb B
0|12
 1 1 2 1 2 1 2 1 2 1 2 1 2
 0 1 2 4 5 7 8 10 11 13 14 16 17
 C C# Db D# Eb E# F Gb G Ab A Bb B


Godzilla / Semaphore


godzilla[5] (4L+1s / chroma-positive generator = 4\19 ~= 8/7 ~= 7/6)
UDP
 mode steps
 mode degrees
 note names
4|0
 4 4 4 4 3
 0 4 8 12 16
 C D# F G# Bb
3|1
 4 4 4 3 4
 0 4 8 12 15
 C D# F G# A#
2|2
 4 4 3 4 4
 0 4 8 11 15
 C D# F G A#
1|3
 4 3 4 4 4
 0 4 7 11 15
 C D# E# G A#
0|4
 3 4 4 4 4
 0 3 7 11 15
 C D E# G A#

godzilla[9] (5L+4s / CPG = 15\19 ~= 7/4 ~= 12/7)
UDP
 mode steps
 mode degrees
 note names
8|0
 3 3 1 3 1 3 1 3 1
 0 3 6 7 10 11 14 15 18
 C D E E# Gb G A A# B#
7|1
 3 1 3 3 1 3 1 3 1
 0 3 4 7 10 11 14 15 18
 C D D# E# Gb G A A# B#
6|2
 3 1 3 1 3 3 1 3 1
 0 3 4 7 8 11 14 15 18
 C D D# E# F G A A# B#
5|3
 3 1 3 1 3 1 3 3 1
 0 3 4 7 8 11 12 15 18
 C D D# E# F G G# A# B#
4|4
 3 1 3 1 3 1 3 1 3
 0 3 4 7 8 11 12 15 16
 C D D# E# F G G# A# Bb
3|5
 1 3 3 1 3 1 3 1 3
 0 1 4 7 8 11 12 15 16
 C C# D# E# F G G# A# Bb
2|6
 1 3 1 3 3 1 3 1 3
 0 1 4 5 8 11 12 15 16
 C C# D# Eb F G G# A# Bb
1|7
 1 3 1 3 1 3 3 1 3
 0 1 4 5 8 9 12 15 16
 C C# D# Eb F F# G# A# Bb
0|8
 1 3 1 3 1 3 1 3 3
 0 1 4 5 8 9 12 13 16
 C C# D# Eb F F# G# Ab Bb

godzilla[14] (5L+9s / CPG = 4\19)
UDP
 steps
 degrees
 note names
13|0
 2 1 2 1 1 2 1 1 2 1 1 2 1 1
 0 2 3 5 6 7 9 10 11 13 14 15 17 18
 C Db D Eb E E# F# Gb G Ab A A# B B#
12|1
 2 1 1 2 1 2 1 1 2 1 1 2 1 1
 0 2 3 4 6 7 9 10 11 13 14 15 17 18
 C Db D D# E E# F# Gb G Ab A A# B B#
11|2
 2 1 1 2 1 1 2 1 2 1 1 2 1 1
 0 2 3 4 6 7 8 10 11 13 14 15 17 18
 C Db D D# E E# F Gb G Ab A A# B B#
10|3
 2 1 1 2 1 1 2 1 1 2 1 2 1 1
 0 2 3 4 6 7 8 10 11 12 14 15 17 18
 C Db D D# E E# F Gb G G# A A# B B#
9|4
 2 1 1 2 1 1 2 1 1 2 1 1 2 1
 0 2 3 4 6 7 8 10 11 12 14 15 16 18
 C Db D D# E E# F Gb G G# A A# Bb B#
8|5
 1 2 1 2 1 1 2 1 1 2 1 1 2 1
 0 1 3 4 6 7 8 10 11 12 14 15 16 18
 C C# D D# E E# F Gb G G# A A# Bb B#
7|6
 1 2 1 1 2 1 2 1 1 2 1 1 2 1
 0 1 3 4 5 7 8 10 11 12 14 15 16 18
 C C# D D# Eb E# F Gb G G# A A# Bb B#
6|7
 1 2 1 1 2 1 1 2 1 2 1 1 2 1
 0 1 3 4 5 7 8 9 11 12 14 15 16 18
 C C# D D# Eb E# F F# G G# A A# Bb B#
5|8
 1 2 1 1 2 1 1 2 1 1 2 1 2 1
 0 1 3 4 5 7 8 9 11 12 13 15 16 18
 C C# D D# Eb E# F F# G G# Ab A# Bb B#
4|9
 1 2 1 1 2 1 1 2 1 1 2 1 1 2
 0 1 3 4 5 7 8 9 11 12 13 15 16 17
 C C# D D# Eb E# F F# G G# Ab A# Bb B
3|10
 1 1 2 1 2 1 1 2 1 1 2 1 1 2
 0 1 2 4 5 7 8 9 11 12 13 15 16 17
 C C# Db D# Eb E# F F# G G# Ab A# Bb B
2|11
 1 1 2 1 1 2 1 2 1 1 2 1 1 2
 0 1 2 4 5 6 8 9 11 12 13 15 16 17
 C C# Db D# Eb E F F# G G# Ab A# Bb B
1|12
 1 1 2 1 1 2 1 1 2 1 2 1 1 2
 0 1 2 4 5 6 8 9 10 12 13 15 16 17
 C C# Db D# Eb E F F# Gb G# Ab A# Bb B
0|13
 1 1 2 1 1 2 1 1 2 1 1 2 1 2
 0 1 2 4 5 6 8 9 10 12 13 14 16 17
 C C# Db D# Eb E F F# Gb G# Ab A Bb B


Kleismic / Hanson


kleismic[7] (4L+3s / chroma-positive generator = 14\19 ~= 5/3)
UDP
 steps
 degrees
 note names
 comments
6|0
 4 4 1 4 1 4 1
 0 4 8 9 13 14 18
 C D# F F# Ab A B#
 has 4/3
5|1
 4 1 4 4 1 4 1
 0 4 5 9 13 14 18
 C D# Eb F# Ab A B#
4|2
 4 1 4 1 4 4 1
 0 4 5 9 10 14 18
 C D# Eb F# Gb A B#
3|3
 4 1 4 1 4 1 4
 0 4 5 9 10 14 15
 C D# Eb F# Gb A A#
 symmetrical
2|4
 1 4 4 1 4 1 4
 0 1 5 9 10 14 15
 C C# Eb F# Gb A A#
1|5
 1 4 1 4 4 1 4
 0 1 5 6 10 14 15
 C C# Eb E Gb A A#
0|6
 1 4 1 4 1 4 4
 0 1 5 6 10 11 15
 C C# Eb E Gb G A#
 has 3/2

kleismic[11] (4L+7s / CPG = 14\19)
UDP
 steps
 degrees
 note names
 comments
10|0
 3 1 3 1 1 3 1 1 3 1 1
 0 3 4 7 8 9 12 13 14 17 18
 C D D# E# F F# G# Ab A B B#
9|1
 3 1 1 3 1 3 1 1 3 1 1
 0 3 4 5 8 9 12 13 14 17 18
 C D D# Eb F F# G# Ab A B B#
8|2
 3 1 1 3 1 1 3 1 3 1 1
 0 3 4 5 8 9 10 13 14 17 18
 C D D# Eb F F# Gb Ab A B B#
7|3
 3 1 1 3 1 1 3 1 1 3 1
 0 3 4 5 8 9 10 13 14 15 18
 C D D# Eb F F# Gb Ab A A# B#
6|4
 1 3 1 3 1 1 3 1 1 3 1
 0 1 4 5 8 9 10 13 14 15 18
 C C# D# Eb F F# Gb Ab A A# B#
5|5
 1 3 1 1 3 1 3 1 1 3 1
 0 1 4 5 6 9 10 13 14 15 18
 C C# D# Eb E F# Gb Ab A A# B#
 symmetrical, has neither 4/3 nor 3/2
4|6
 1 3 1 1 3 1 1 3 1 3 1
 0 1 4 5 6 9 10 11 14 15 18
 C C# D# Eb E F# Gb G A A# B#
3|7
 1 3 1 1 3 1 1 3 1 1 3
 0 1 4 5 6 9 10 11 14 15 16
 C C# D# Eb E F# Gb G A A# Bb
2|8
 1 1 3 1 3 1 1 3 1 1 3
 0 1 2 5 6 9 10 11 14 15 16
 C C# Db Eb E F# Gb G A A# Bb
1|9
 1 1 3 1 1 3 1 3 1 1 3
 0 1 2 5 6 7 10 11 14 15 16
 C C# Db Eb E E# Gb G A A# Bb
0|10
 1 1 3 1 1 3 1 1 3 1 3
 0 1 2 5 6 7 10 11 12 15 16
 C C# Db Eb E E# Gb G G# A# Bb

kleismic[15] (4L+11s / CPG = 14\19)
UDP
 steps
 degrees
 note names
14|0
 2 1 1 2 1 1 1 2 1 1 1 2 1 1 1
 0 2 3 4 6 7 8 9 11 12 13 14 16 17 18
 C Db D D# E E# F F# G G# Ab A Bb B B#
13|1
 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1
 0 2 3 4 5 7 8 9 11 12 13 14 16 17 18
 C Db D D# Eb E# F F# G G# Ab A Bb B B#
12|2
 2 1 1 1 2 1 1 1 2 1 1 2 1 1 1
 0 2 3 4 5 7 8 9 10 12 13 14 16 17 18
 C Db D D# Eb E# F F# Gb G# Ab A Bb B B#
11|3
 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1
 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18
 C Db D D# Eb E# F F# Gb G# Ab A A# B B#
10|4
 1 2 1 1 2 1 1 1 2 1 1 1 2 1 1
 0 1 3 4 5 7 8 9 10 12 13 14 15 17 18
 C C# D D# Eb E# F F# Gb G# Ab A A# B B#
9|5
 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1
 0 1 3 4 5 6 8 9 10 12 13 14 15 17 18
 C C# D D# Eb E F F# Gb G# Ab A A# B B#
8|6
 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1
 0 1 3 4 5 6 8 9 10 11 13 14 15 17 18
 C C# D D# Eb E F F# Gb G Ab A A# B B#
7|7
 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
 0 1 3 4 5 6 8 9 10 11 13 14 15 16 18
 C C# D D# Eb E F F# Gb G Ab A A# Bb B#
6|8
 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1
 0 1 2 4 5 6 8 9 10 11 13 14 15 16 18
 C C# Db D# Eb E F F# Gb G Ab A A# Bb B#
5|9
 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1
 0 1 2 4 5 6 7 9 10 11 13 14 15 16 18
 C C# Db D# Eb E E# F# Gb G Ab A A# Bb B#
4|10
 1 1 2 1 1 1 2 1 1 1 2 1 1 2 1
 0 1 2 4 5 6 7 9 10 11 12 14 15 16 18
 C C# Db D# Eb E E# F# Gb G G# A A# Bb B#
3|11
 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2
 0 1 2 4 5 6 7 9 10 11 12 14 15 16 17
 C C# Db D# Eb E E# F# Gb G G# A A# Bb B
2|12
 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2
 0 1 2 3 5 6 7 9 10 11 12 14 15 16 17
 C C# Db D Eb E E# F# Gb G G# A A# Bb B
1|13
 1 1 1 2 1 1 1 2 1 1 2 1 1 1 2
 0 1 2 3 5 6 7 8 10 11 12 14 15 16 17
 C C# Db D Eb E E# F Gb G G# A A# Bb B
0|14
 1 1 1 2 1 1 1 2 1 1 1 2 1 1 2
 0 1 2 3 5 6 7 8 10 11 12 13 15 16 17
 C C# Db D Eb E E# F Gb G G# Ab A# Bb B


Magic


magic[7] (3L+4s / chroma-positive generator = 6\19 ~=5/4)
UDP
 steps
 degrees
 note names
6|0
 5 1 5 1 5 1 1
 0 5 6 11 12 17 18
 C Eb E G G# B B#
5|1
 5 1 5 1 1 5 1
 0 5 6 11 12 13 18
 C Eb E G G# Ab B#
4|2
 5 1 1 5 1 5 1
 0 5 6 7 12 13 18
 C Eb E E# G# Ab B#
3|3
 1 5 1 5 1 5 1
 0 1 6 7 12 13 18
 C C# E E# G# Ab B#
2|4
 1 5 1 5 1 1 5
 0 1 6 7 12 13 14
 C C# E E# G# Ab A
1|5
 1 5 1 1 5 1 5
 0 1 6 7 8 13 14
 C C# E E# F Ab A
0|6
 1 1 5 1 5 1 5
 0 1 2 7 8 13 14
 C C# Db E# F Ab A

magic[10] (3L+7s / CPG = 6\19)
UDP
 steps
 degrees
 note names
9|0
 4 1 1 4 1 1 4 1 1 1
 0 4 5 6 10 11 12 16 17 18
 C D# Eb E Gb G G# Bb B B#
8|1
 4 1 1 4 1 1 1 4 1 1
 0 4 5 6 10 11 12 13 17 18
 C D# Eb E Gb G G# Ab B B#
7|2
 4 1 1 1 4 1 1 4 1 1
 0 4 5 6 7 11 12 13 17 18
 C D# Eb E E# G G# Ab B B#
6|3
 1 4 1 1 4 1 1 4 1 1
 0 1 5 6 7 11 12 13 17 18
 C C# Eb E E# G G# Ab B B#
5|4
 1 4 1 1 4 1 1 1 4 1
 0 1 5 6 7 11 12 13 14 18
 C C# Eb E E# G G# Ab A B#
4|5
 1 4 1 1 1 4 1 1 4 1
 0 1 5 6 7 8 12 13 14 18
 C C# Eb E E# F G# Ab A B#
3|6
 1 1 4 1 1 4 1 1 4 1
 0 1 2 6 7 8 12 13 14 18
 C C# Db E E# F G# Ab A B#
2|7
 1 1 4 1 1 4 1 1 1 4
 0 1 2 6 7 8 12 13 14 15
 C C# Db E E# F G# Ab A A#
1|8
 1 1 4 1 1 1 4 1 1 4
 0 1 2 6 7 8 9 13 14 15
 C C# Db E E# F F# Ab A A#
0|9
 1 1 1 4 1 1 4 1 1 4
 0 1 2 3 7 8 9 13 14 15
 C C# Db D E# F F# Ab A A#

magic[13] (3L+10s / CPG = 6\19 ~=5/4)
UDP
 steps
 degrees
 note names
12|0
 3 1 1 1 3 1 1 1 3 1 1 1 1
 0 3 4 5 6 9 10 11 12 15 16 17 18
 C D D# Eb E F# Gb G G# A# Bb B B#
11|1
 3 1 1 1 3 1 1 1 1 3 1 1 1
 0 3 4 5 6 9 10 11 12 13 16 17 18
 C D D# Eb E F# Gb G G# Ab Bb B B#
10|2
 3 1 1 1 1 3 1 1 1 3 1 1 1
 0 3 4 5 6 7 10 11 12 13 16 17 18
 C D D# Eb E E# Gb G G# Ab Bb B B#
9|3
 1 3 1 1 1 3 1 1 1 3 1 1 1
 0 1 4 5 6 7 10 11 12 13 16 17 18
 C C# D# Eb E E# Gb G G# Ab Bb B B#
8|4
 1 3 1 1 1 3 1 1 1 1 3 1 1
 0 1 4 5 6 7 10 11 12 13 14 17 18
 C C# D# Eb E E# Gb G G# Ab A B B#
7|5
 1 3 1 1 1 1 3 1 1 1 3 1 1
 0 1 4 5 6 7 8 11 12 13 14 17 18
 C C# D# Eb E E# F G G# Ab A B B#
6|6
 1 1 3 1 1 1 3 1 1 1 3 1 1
 0 1 2 5 6 7 8 11 12 13 14 17 18
 C C# Db Eb E E# F G G# Ab A B B#
5|7
 1 1 3 1 1 1 3 1 1 1 1 3 1
 0 1 2 5 6 7 8 11 12 13 14 15 18
 C C# Db Eb E E# F G G# Ab A A# B#
4|8
 1 1 3 1 1 1 1 3 1 1 1 3 1
 0 1 2 5 6 7 8 9 12 13 14 15 18
 C C# Db Eb E E# F F# G# Ab A A# B#
3|9
 1 1 1 3 1 1 1 3 1 1 1 3 1
 0 1 2 3 6 7 8 9 12 13 14 15 18
 C C# Db D E E# F F# G# Ab A A# B#
2|10
 1 1 1 3 1 1 1 3 1 1 1 1 3
 0 1 2 3 6 7 8 9 12 13 14 15 16
 C C# Db D E E# F F# G# Ab A A# Bb
1|11
 1 1 1 3 1 1 1 1 3 1 1 1 3
 0 1 2 3 6 7 8 9 10 13 14 15 16
 C C# Db D E E# F F# Gb Ab A A# Bb
0|12
 1 1 1 1 3 1 1 1 3 1 1 1 3
 0 1 2 3 4 7 8 9 10 13 14 15 16
 C C# Db D D# E# F F# Gb Ab A A# Bb

magic[16] (3L+13s / CPG = 6\19)
UDP
 steps
 degrees
 note names
15|0
 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
 0 2 3 4 5 6 8 9 10 11 12 14 15 16 17 18
 C Db D D# Eb E F F# Gb G G# A A# Bb B B#
14|1
 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
 0 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18
 C Db D D# Eb E F F# Gb G G# Ab A# Bb B B#
13|2
 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1
 0 2 3 4 5 6 7 9 10 11 12 13 15 16 17 18
 C Db D D# Eb E E# F# Gb G G# Ab A# Bb B B#
12|3
 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1
 0 1 3 4 5 6 7 9 10 11 12 13 15 16 17 18
 C C# D D# Eb E E# F# Gb G G# Ab A# Bb B B#
11|4
 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1
 0 1 3 4 5 6 7 9 10 11 12 13 14 16 17 18
 C C# D D# Eb E E# F# Gb G G# Ab A Bb B B#
10|5
 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1
 0 1 3 4 5 6 7 8 10 11 12 13 14 16 17 18
 C C# D D# Eb E E# F Gb G G# Ab A Bb B B#
9|6
 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
 0 1 2 4 5 6 7 8 10 11 12 13 14 16 17 18
 C C# Db D# Eb E E# F Gb G G# Ab A Bb B B#
8|7
 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1
 0 1 2 4 5 6 7 8 10 11 12 13 14 15 17 18
 C C# Db D# Eb E E# F Gb G G# Ab A A# B B#
7|8
 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1
 0 1 2 4 5 6 7 8 9 11 12 13 14 15 17 18
 C C# Db D# Eb E E# F F# G G# Ab A A# B B#
6|9
 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1
 0 1 2 3 5 6 7 8 9 11 12 13 14 15 17 18
 C C# Db D Eb E E# F F# G G# Ab A A# B B#
5|10
 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1
 0 1 2 3 5 6 7 8 9 11 12 13 14 15 16 18
 C C# Db D Eb E E# F F# G G# Ab A A# Bb B#
4|11
 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1
 0 1 2 3 5 6 7 8 9 10 12 13 14 15 16 18
 C C# Db D Eb E E# F F# Gb G# Ab A A# Bb B#
3|12
 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1
 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 18
 C C# Db D D# E E# F F# Gb G# Ab A A# Bb B#
2|13
 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2
 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17
 C C# Db D D# E E# F F# Gb G# Ab A A# Bb B
1|14
 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2
 0 1 2 3 4 6 7 8 9 10 11 13 14 15 16 17
 C C# Db D D# E E# F F# Gb G Ab A A# Bb B
0|15
 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2
 0 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17
 C C# Db D D# Eb E# F F# Gb G Ab A A# Bb B

Sensi


sensi[5] (3L+2s / chroma-positive generator = 12\19)
UDP
 mode steps
 mode degrees
 note names
4|0
 5 5 2 5 2
 0 5 10 12 17
 C Eb Gb G# B
3|1
 5 2 5 5 2
 0 5 7 12 17
 C Eb E# G# B
2|2
 5 2 5 2 5
 0 5 7 12 14
 C Eb E# G# A
1|3
 2 5 5 2 5
 0 2 7 12 14
 C Db E# G# A
0|4
 2 5 2 5 5
 0 2 7 9 14
 C Db E# F# A

sensi[8] (3L+5s / CPG = 12\19)
UDP
 mode steps
 mode degrees
 note names
7|0
 3 2 3 2 2 3 2 2
 0 3 5 8 10 12 15 17
 C D Eb F Gb G# A# B
6|1
 3 2 2 3 2 3 2 2
 0 3 5 7 10 12 15 17
 C D Eb E# Gb G# A# B
5|2
 3 2 2 3 2 2 3 2
 0 3 5 7 10 12 14 17
 C D Eb E# Gb G# A B
4|3
 2 3 2 3 2 2 3 2
 0 2 5 7 10 12 14 17
 C Db Eb E# Gb G# A B
3|4
 2 3 2 2 3 2 3 2
 0 2 5 7 9 12 14 17
 C Db Eb E# F# G# A B
2|5
 2 3 2 2 3 2 2 3
 0 2 5 7 9 12 14 16
 C Db Eb E# F# G# A Bb
1|6
 2 2 3 2 3 2 2 3
 0 2 4 7 9 12 14 16
 C Db D# E# F# G# A Bb
0|7
 2 2 3 2 2 3 2 3
 0 2 4 7 9 11 14 16
 C Db D# E# F# G A Bb

sensi[11] (8L+3s / CPG = 7\19)
UDP
 mode steps
 mode degrees
 note names
10|0
 2 2 2 1 2 2 2 1 2 2 1
 0 2 4 6 7 9 11 13 14 16 18
 C Db D# E E# F# G Ab A Bb B#
9|1
 2 2 2 1 2 2 1 2 2 2 1
 0 2 4 6 7 9 11 12 14 16 18
 C Db D# E E# F# G G# A Bb B#
8|2
 2 2 1 2 2 2 1 2 2 2 1
 0 2 4 5 7 9 11 12 14 16 18
 C Db D# Eb E# F# G G# A Bb B#
7|3
 2 2 1 2 2 2 1 2 2 1 2
 0 2 4 5 7 9 11 12 14 16 17
 C Db D# Eb E# F# G G# A Bb B
6|4
 2 2 1 2 2 1 2 2 2 1 2
 0 2 4 5 7 9 10 12 14 16 17
 C Db D# Eb E# F# Gb G# A Bb B
5|5
 2 1 2 2 2 1 2 2 2 1 2
 0 2 3 5 7 9 10 12 14 16 17
 C Db D Eb E# F# Gb G# A Bb B
4|6
 2 1 2 2 2 1 2 2 1 2 2
 0 2 3 5 7 9 10 12 14 15 17
 C Db D Eb E# F# Gb G# A A# B
3|7
 2 1 2 2 1 2 2 2 1 2 2
 0 2 3 5 7 8 10 12 14 15 17
 C Db D Eb E# F Gb G# A A# B
2|8
 1 2 2 2 1 2 2 2 1 2 2
 0 1 3 5 7 8 10 12 14 15 17
 C C# D Eb E# F Gb G# A A# B
1|9
 1 2 2 2 1 2 2 1 2 2 2
 0 1 3 5 7 8 10 12 13 15 17
 C C# D Eb E# F Gb G# Ab A# B
0|10
 1 2 2 1 2 2 2 1 2 2 2
 0 1 3 5 6 8 10 12 13 15 17
 C C# D Eb E F Gb G# Ab A# B


Liese / Triton


liese[5] (2L+3s / chroma-positive generator = 9\19 ~= 7/5)
UDP
 steps
 degrees
 note names
4|0
 8 1 8 1 1
 0 8 9 17 18
 C F F# B B#
3|1
 8 1 1 8 1
 0 8 9 10 18
 C F F# Gb B#
2|2
 1 8 1 8 1
 0 1 9 10 18
 C C# F# Gb B#
1|3
 1 8 1 1 8
 0 1 9 10 11
 C C# F# Gb G
0|4
 1 1 8 1 8
 0 1 2 10 11
 C C# Db Gb G

liese[7] (2L+5s / CPG = 9\19)
UDP
 steps
 degrees
 note names
6|0
 7 1 1 7 1 1 1
 0 7 8 9 16 17 18
 C E# F F# Bb B B#
5|1
 7 1 1 1 7 1 1
 0 7 8 9 10 17 18
 C E# F F# Gb B B#
4|2
 1 7 1 1 7 1 1
 0 1 8 9 10 17 18
 C C# F F# Gb B B#
3|3
 1 7 1 1 1 7 1
 0 1 8 9 10 11 18
 C C# F F# Gb G B#
2|4
 1 1 7 1 1 7 1
 0 1 2 9 10 11 18
 C C# Db F# Gb G B#
1|5
 1 1 7 1 1 1 7
 0 1 2 9 10 11 12
 C C# Db F# Gb G G#
0|6
 1 1 1 7 1 1 7
 0 1 2 3 10 11 12
 C C# Db D Gb G G#

liese[9] (2L+7s / CPG = 9\19)
UDP
 steps
 degrees
 note names
8|0
 6 1 1 1 6 1 1 1 1
 0 6 7 8 9 15 16 17 18
 C E E# F F# A# Bb B B#
7|1
 6 1 1 1 1 6 1 1 1
 0 6 7 8 9 10 16 17 18
 C E E# F F# Gb Bb B B#
6|2
 1 6 1 1 1 6 1 1 1
 0 1 7 8 9 10 16 17 18
 C C# E# F F# Gb Bb B B#
5|3
 1 6 1 1 1 1 6 1 1
 0 1 7 8 9 10 11 17 18
 C C# E# F F# Gb G B B#
4|4
 1 1 6 1 1 1 6 1 1
 0 1 2 8 9 10 11 17 18
 C C# Db F F# Gb G B B#
3|5
 1 1 6 1 1 1 1 6 1
 0 1 2 8 9 10 11 12 18
 C C# Db F F# Gb G G# B#
2|6
 1 1 1 6 1 1 1 6 1
 0 1 2 3 9 10 11 12 18
 C C# Db D F# Gb G G# B#
1|7
 1 1 1 6 1 1 1 1 6
 0 1 2 3 9 10 11 12 13
 C C# Db D F# Gb G G# Ab
0|8
 1 1 1 1 6 1 1 1 6
 0 1 2 3 4 10 11 12 13
 C C# Db D D# Gb G G# Ab

liese[11] (2L+9s / CPG = 9\19)
UDP
 steps
 degrees
 note names
10|0
 5 1 1 1 1 5 1 1 1 1 1
 0 5 6 7 8 9 14 15 16 17 18
 C Eb E E# F F# A A# Bb B B#
9|1
 5 1 1 1 1 1 5 1 1 1 1
 0 5 6 7 8 9 10 15 16 17 18
 C Eb E E# F F# Gb A# Bb B B#
8|2
 1 5 1 1 1 1 5 1 1 1 1
 0 1 6 7 8 9 10 15 16 17 18
 C C# E E# F F# Gb A# Bb B B#
7|3
 1 5 1 1 1 1 1 5 1 1 1
 0 1 6 7 8 9 10 11 16 17 18
 C C# E E# F F# Gb G Bb B B#
6|4
 1 1 5 1 1 1 1 5 1 1 1
 0 1 2 7 8 9 10 11 16 17 18
 C C# Db E# F F# Gb G Bb B B#
5|5
 1 1 5 1 1 1 1 1 5 1 1
 0 1 2 7 8 9 10 11 12 17 18
 C C# Db E# F F# Gb G G# B B#
4|6
 1 1 1 5 1 1 1 1 5 1 1
 0 1 2 3 8 9 10 11 12 17 18
 C C# Db D F F# Gb G G# B B#
3|7
 1 1 1 5 1 1 1 1 1 5 1
 0 1 2 3 8 9 10 11 12 13 18
 C C# Db D F F# Gb G G# Ab B#
2|8
 1 1 1 1 5 1 1 1 1 5 1
 0 1 2 3 4 9 10 11 12 13 18
 C C# Db D D# F# Gb G G# Ab B#
1|9
 1 1 1 1 5 1 1 1 1 1 5
 0 1 2 3 4 9 10 11 12 13 14
 C C# Db D D# F# Gb G G# Ab A
0|10
 1 1 1 1 1 5 1 1 1 1 5
 0 1 2 3 4 5 10 11 12 13 14
 C C# Db D D# Eb Gb G G# Ab A

MOS scales of sizes 13, 15, and 17 also exist, and follow a similar pattern:
liese[13] 4111114111111 etc.
liese[15] 311111131111111 etc.
liese[17] 21111111211111111 etc.